BEIJING (Reuters) - China's factory downturn worsened in June as a key activity index hit a seven-month low, data expected to raise expectations the central bank may seek more policy easing to revive the world's second-largest economy.

The official Chinese purchasing managers' index (PMI) fell to 50.2 in June after seasonal adjustments, the National Bureau of Statistics said on Sunday, above forecasts for 49.8, but down from May's 50.4.

That was the worse reading since November last year, and a sharp fall in export orders and shrinking new orders suggested a recovery is not in sight. This would fuel bets that Beijing could further relax monetary policy as soon as this month, an analyst said.

"New orders and input prices are still falling, which show there are still many factors affecting production. A recovery in industrial output would take time," Zhang Liqun, a government researcher, said in a statement accompanying the PMI data.

Zhang's cautious tone backed estimates among some analysts that China's economy could worsen in the third quarter as previous policy easing takes time to filter through, potentially jeopardizing Beijing's 2012 growth target of 7.5 percent.

A protracted slowdown in China would further hobble a world economy already bruised by Europe's nagging debt crisis, and an ailing U.S. economic recovery. It is also a headache for Beijing as exporters are mainstay employers in China.

Sunday's PMI suggested Chinese factories struggled with lackluster foreign and domestic demand in June.

The sub-index for new export orders had its biggest monthly fall since December, shedding 2.9 percentage points to 47.5. New orders, which include domestic orders, slipped 0.6 percentage points to 49.2.

This means factories received fewer orders in June from May as the 50-point level separates expansion from contraction.

The dour numbers underline worries that China may miss its 2012 target to grow imports and exports by 10 percent, a level Trade Minister Chen Deming said would be met only if the country is "lucky".

Economists are not counting on it. A Reuters poll in May showed they expect China's economy to clock its worse annual growth in 13 years this year at 8.2 percent.

IMMINENT RRR CUT?

As China heads into its once-a-decade leadership change later this year, Beijing -- which believes strong growth legitimizes its rule -- is eager to do what it can to keep the economy growing briskly.

With China's inflation likely to stay benign, Beijing has room to act. The country's annual inflation ran at 3 percent in May, below a 2012 target of 4 percent. The PMI input prices sub-index stood at 3-1/2-year lows of 41.2 in June.

To shore up growth, Beijing lowered interest rates once and reduced banks' reserve requirement ratio (RRR) twice this year.

Traders said on Friday they anticipate the central bank to lower banks' RRR soon to ease a recent liquidity squeeze, triggered by regulatory requirements and a large initial public offering.

Small Chinese firms have also complained that loans are hard to come by despite lower lending rates. They say tight credit conditions further aggravate sluggish business.

Sunday's PMI showed the smallest Chinese factories were indeed hardest hit. The PMI for small businesses languished under 50 for the third straight month at 47.2. The PMI for big factories stood at 50.6, and that for mid-sized companies at 50.

But Hua Zhongwei, an economist at Huachuang Securities, was hopeful of an imminent recovery. He expects economic growth to trough at around 7.8 percent in the second quarter, before quickening to 8 percent over the next three months.

"The government and banks will ratchet up support for growth and we could see some impact from their efforts in the third quarter," Hua said.

(Reporting by Koh Gui Qing; Additional reporting by Kevin Yao; Editing by Ed Lane)